A Hybridisable Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion-Reaction Equations

Abstract

A hybridisable discontinuous Galerkin (HDG) discretisation of time-dependent linear convection-diffusion-reaction equations is considered. For the space discretisation, the HDG method uses piecewise polynomials of degrees $k$ ≥ 0 to approximate potential $u$ and its trace on the inter-element boundaries, and the flux is approximated by piecewise polynomials of degree max{$k$ − 1, 0}, $k$ ≥ 0. In the fully discrete scheme, the time derivative is approximated by the backward Euler difference. Error estimates obtained for semi-discrete and fully discrete schemes show that the HDG method converges uniformly with respect to the equation coefficients. Numerical examples confirm the theoretical results.